In the delivery of medical liquids, such as medication, drugs, chemotherapeutic agents, intravenous solutions or the like, it is known to use a flow control valve that permits the user to select a particular flow rate from a range of discrete flow rates. One such flow control valve, which uses glass capillary structures to control the flow rate, is described in U.S. Pat. No. 6,273,133 entitled “Fluid Flow Rate Switching Device.” The device shown there has two internal passageways, each with a glass capillary structure that limits flow through the passageway. A valve member directs fluid flow through either or both of the passageways to provide several different flow rates through the flow control device. While this device works satisfactorily, the use of glass capillary structures can add to the cost and there is a desire to have flow control devices with a greater selection of available flow rates. Although this is but one example, there continues to be a need for medical fluid flow control valves that address one or more of the drawbacks found in prior valves.